I present you the HREarth:
Started as Bohemia in 1399 and decided after inheriting Poland and Hungary, well, why not do a WC with this? This was my first try and also my first time uniting the HRE. I know I could have been faster (it's 1737), but I made some bad decisions (e.g. attacked Japan too late) and had some bad luck (regency councils -.-).
The new world is completely Czech (except one Cherokee province which was already catholic for some reason...), the steppes are largely Czech cultured and the Czech culture did become quite large in Middle Europe, especially Bavaria, Poland and Hungary are largely Czech cultured. Every province of Middle Europe has a manufactory, too, I just had way too much money (had my army and navy close to the force limit most of the time, more than 1,5 million soldiers).
I won't ever go Aristocratic and Serfdom again. I had 3 times the Time of Troubles event which is just plain annoying. Being Narrowminded, Serfdom and having CAD however allowed me to still regain stability in one month, which is pretty good in a world spanning empire...
There are 1 Protestant and 3 Shinto provinces left, all of which have 25% chance to convert to catholic, so a World Conversion is not that far away.